ANALYSING CYCLES in Biology and Medicine—a practical introduction to Circular Variables & Periodic Regression
2nd edition, 2008: ISBN 978-0-9736209-2-4
Author: K.N.I. Bell, B.Sc., M.Sc., Ph.D.
About 180 pages, 70,000 words, copiously illustrated. See sample excerpt (below) for an idea of what is in it; and see (download) selected papers (1995, 1997, 2001a, 2001b) for examples of its application.
See review by F. J. Rohlf (of "Biometry", Sokal & Rohlf) in Quarterly Review of Biology 85 (1):123 (March 2010)
Motivation for this book: to improve how biologists typically handle cyclic or periodic data.
Cycles are pervasive in biology, yet often improperly analysed (e.g. by dividing a year into seasons and analysing via factorial Anova that by definition cannot use their sequentiality), or more generally ignored and treated as no more than a nuisance. That is for lack of knowing the proper analytical methods. C.I. Bliss stated the problem:
“Periodic phenomena in biology and climatology occur so widely that we tend either to adapt to them as unavoidable nuisances or are overimpressed by their day to day deviations. We can’t see the forest for the trees” -- C.I. Bliss, 1958.
To overcome that problem, the book explains the techniques and the background vividly and graphically, making periodic regression accessible to all readers.
Back Cover text:
Cycles surround us. Indeed, they are the essence of life, and critically important in biology and medicine. We need to know how to analyse and understand them.
But, too often, researchers are given ugly advice: to keep cycles out of data—by restricting sampling to the same time of day, tide, etc. That’s a bad plan; it’s costly because you have to wait for your chosen special times (e.g. 1100h), and even more costly with multiple cycles because you have to wait for rare conjunctions of special times (e.g. 1100h + high tide) in each. The final consequence is: no matter how carefully you worked, the opportunity to describe key cycles is lost, so your findings are virtually meaningless because they can’t be generalised outside the special times you chose.
In fact, it is easier, more useful, and much more beautiful, to put cycles into the analysis than to keep them out of the data. This book makes it easy.
Written in a relaxed style, the book anticipates readers ranging from apprehensive to advanced. It is copiously illustrated with conceptual diagrams and worked-out examples. It contains all that’s needed to get started: even the basic trigonometry and a crisp stats refresher. All you need is the book, your data, and Excel or a stats package.
Periodic regression is so sparsely known to biologists (writ large) that to many it seems almost witchcraft. This situation will no doubt continue for some years, and during that time it will be necessary to reference it carefully or even explain it directly so that readers (and reviewers) can understand that it is a direct extension of regression, and understand its application to removing common sets of periodic trends from parallel sets of data to enable comparisons that would be impossible or unreliable otherwise.
No comparable book exists. Its key precedents (Bliss 1958, 1970 and Batschelet 1981) are out of print. Bliss (1958) is a beautiful paper that comes the closest to making periodic regression readily accessible but, like the others and understandably for its time, does not anticipate the availability of software for analysis and data handling. "Analysing Cycles ..." graphically presents the conceptual framework and simplifies notation for expression and implementation of periodic regression..
The First Edition (2004) was an e-book titled: Introduction to Circular Variables & Periodic Regression in Biology (e-book in PDF format): ISBN 0-9736209-0-0. It is on deposit at the National Library of Canada, but that version is no longer distributed and at present no electronic version of the 2nd Edition is planned.
Batschelet, E. 1981. Circular statistics in biology. Mathematics in Biology,
R. Sibson & J. Cohen (Ser. Ed.). London: Academic Press. xvi+371 pp.
Bliss, C. I. 1958. Periodic regression in biology and climatology. Bull. Conn. Agric. Exp. Station, New Haven 615: 1-55.
Bliss, C. I. 1970. Statistics in Biology, Vol. 2. New York: McGraw-Hill. 639 pp.